Averaging theory at any order for computing periodic orbits

PHYSICA D-NONLINEAR PHENOMENA

卷:250

Article

Gine, Jaume¹  Grau, Maite¹  Llibre, Jaume² 

[1] Univ Lleida, Dept Matemat, Lleida 25001, Catalonia, Spain

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

关键词: First-order analytic differential equations;    Averaging theory;    Polynomial differential equations;    Limit cycles;    Periodic orbits;   

DOI  :  10.1016/j.physd.2013.01.015

来源: Elsevier

【 摘 要 】

We provide a recurrence formula for the coefficients of the powers of a in the series expansion of the solutions around epsilon = 0 of the perturbed first-order differential equations. Using it, we give an averaging theory at any order in epsilon for the following two kinds of analytic differential equation: dx/d theta = Sigma(k >= 1) epsilon F-k(k)(theta, x), dx/d theta = Sigma(k >= 0) epsilon F-k(k)(theta,x). A planar polynomial differential system with a singular point at the origin can be transformed, using polar coordinates, to an equation of the previous form. Thus, we apply our results for studying the limit cycles of a planar polynomial differential systems. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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